On embeddability of joins and their `factors'
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866918274277572608 |
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| author | Parsa, S. Skopenkov, A. |
| author_facet | Parsa, S. Skopenkov, A. |
| contents | We present a short and clear proof of the following particular case of a 2006 result of Melikhov-Schepin: Let $K$ be a $k$-dimensional simplicial complex and $K*[3]$ the union of three cones over $K$ along their common bases. If $2d\ge3k+3$ and $K*[3]$ embeds into $\mathbb R^{d+2}$, then $K$ embeds into $\mathbb R^d$.
We also present a generalization of this theorem. The proofs are based on the Haefliger-Weber `configuration spaces' embeddability criterion, equivariant suspension theorem and simple properties of joins and cones. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2003_12285 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On embeddability of joins and their `factors' Parsa, S. Skopenkov, A. Geometric Topology 57Q35, 55Q91 We present a short and clear proof of the following particular case of a 2006 result of Melikhov-Schepin: Let $K$ be a $k$-dimensional simplicial complex and $K*[3]$ the union of three cones over $K$ along their common bases. If $2d\ge3k+3$ and $K*[3]$ embeds into $\mathbb R^{d+2}$, then $K$ embeds into $\mathbb R^d$. We also present a generalization of this theorem. The proofs are based on the Haefliger-Weber `configuration spaces' embeddability criterion, equivariant suspension theorem and simple properties of joins and cones. |
| title | On embeddability of joins and their `factors' |
| topic | Geometric Topology 57Q35, 55Q91 |
| url | https://arxiv.org/abs/2003.12285 |